I have moved my web site from http to https, http is fully redirected to https and they are identical in content. I have added both properties to Google Search Console, when I ask Google for crawl (Fetch as Google option in Search console) do I do it for https or for http or for both?
From here on, you should only do these kind of checks (fetch-render, sitemap, crawling, mobile usability etc..) in the HTTPS version of the GSC property.
Side node: You should only monitor the HTTP property in GSC to see if traffic decreases in time. And at some point, you should have no traffic data in the HTTP property (assuming HTTP site is correctly redirected to HTTPS)